Multipolar potentials and weighted Hardy inequalities

2022/12/01 by Canale, A.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.00835

Abstract

\beginabstract In this paper we state the following weighted Hardy type inequality for any functions φ in a weighted Sobolev space and for weight functions μ of a quite general type c_N,μ ∫_\R^NV φ²μ(x)dx≤ ∫_\R^N|∇ φ|²μ(x)dx +C_μ∫_\R^NW φ²μ(x)dx, where V is a multipolar potential and W is a bounded function from above depending on μ. The method to get the result is based on the introduction of a suitable vector value function and on an integral identity that we state in the paper. We prove that the constant c_N,μ in the estimate is optimal by building a suitable sequence of functions. \endabstract

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